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We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem (which we call unimodular…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
Satellite mission planning for Earth observation satellites is a combinatorial optimization problem that consists of selecting the optimal subset of imaging requests, subject to constraints, to be fulfilled during an orbit pass of a…
We have an $\m\x\n$ real-valued arbitrary matrix $A$ (e.g. a dictionary) with $\m<\n$ and data $d$ describing the sought-after object with the help of $A$. This work provides an in-depth analysis of the (local and global) minimizers of an…
The design of minimum-compliance bending-resistant structures with continuous cross-section parameters is a challenging task because of its inherent non-convexity. Our contribution develops a strategy that facilitates computing all…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
We derive spherically symmetric solutions of the classical \lambda-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a 3 + 1 decomposition of the…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…
This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information exchange. We first consider a distributed first-order primal-dual…
We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging…
Optimization of quadratic functions and the quotient of those are relevant in subspace and iterative optimization methods. In this paper, the calculation of the generalized operator norm and extremal generalized Rayleigh quotient is…
This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance…
A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following $n$-dimensional quadratic minimization problem in constant time, which is independent of $n$: $z^*=\min_{\mathbf{v} \in…